Answer
$a-\,\,by\,\,\,(commutative\,\,law\,\,for\,\,\cap )\\
b-\,\,by\,\,\,(distributive\,\,law)\\
c-\,\,by\,\,\,(commutative\,\,law\,\,for\,\,\cap) .\\$
Work Step by Step
$For\,\,all\,\,sets\,\,A,\,B,\,and\,C,\\
(A \cup B) \cap C = (A \cap C) \cup (B \cap C).\\
Proof:\,Suppose\,A,\,B,\,and\,C\,are\,any\,sets.\\ Then
(A \cup B) \cap C = C \cap (A\cup B)\,\,\,\,\\by (commutative\,\,law\,\,for\,\,\cap )\\
= (C \cap A) \cup (C \cap B)\,\,\,\,\\by (distributive\,\,law)\\
= (A \cap C) \cup (B \cap C)\,\,\,\,\\by (commutative\,\,law\,\,for\,\,\cap) .\\$